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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stability of transonic shock fronts in two-dimensional Euler systems


Author: Shuxing Chen
Journal: Trans. Amer. Math. Soc. 357 (2005), 287-308
MSC (2000): Primary 35L65, 35L67, 76N10
Published electronically: August 19, 2004
MathSciNet review: 2098096
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Abstract: We study the stability of stationary transonic shock fronts under two-dimensional perturbation in gas dynamics. The motion of the gas is described by the full Euler system. The system is hyperbolic ahead of the shock front, and is a hyperbolic-elliptic composed system behind the shock front. The stability of the shock front and the downstream flow under two-dimensional perturbation of the upstream flow can be reduced to a free boundary value problem of the hyperbolic-elliptic composed system. We develop a method to deal with boundary value problems for such systems. The crucial point is to decompose the system to a canonical form, in which the hyperbolic part and the elliptic part are only weakly coupled in their coefficients. By several sophisticated iterative processes we establish the existence and uniqueness of the solution to the described free boundary value problem. Our result indicates the stability of the transonic shock front and the flow field behind the shock.


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Additional Information

Shuxing Chen
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: sxchen@public8.sta.net.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03698-0
PII: S 0002-9947(04)03698-0
Keywords: Euler system, stability of shock fronts, free boundary problem, hyperbolic-elliptic composed system
Received by editor(s): July 23, 2003
Published electronically: August 19, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.